id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-16,545 |
(4\cdot 11)^{1/2}\cdot 4 = 44^{1/2}\cdot 4
|
923 |
\frac{x}{10} + y/6 + z/7.5 = 1 \Rightarrow 4*z + x*3 + 5*y = 30
|
42,472 |
2^4*5^2*3 = 1200
|
19,402 |
0 - \frac{1}{d^2} = -\dfrac{1}{d^2}
|
11,188 |
\arctan{z_2} = z_1 \Rightarrow z_2 = \tan{z_1}
|
-16,994 |
-6 = -6 \cdot 4 \cdot k - 48 = -24 \cdot k - 48 = -24 \cdot k + 48 \cdot \left(-1\right)
|
-22,302 |
(x + 2(-1)) (x + 9\left(-1\right)) = x^2 - 11 x + 18
|
29,587 |
1 + 3 \times (-1) = 6 \times (-1) + 4
|
10,287 |
1 = a/a\Longrightarrow \frac{1}{1/a} = a
|
-4,765 |
\frac{22\cdot (-1) - x\cdot 8}{x \cdot x + x\cdot 6 + 8} = -\dfrac{3}{2 + x} - \frac{5}{4 + x}
|
-18,433 |
\dfrac{1}{z^2 + 2\times z + 63\times (-1)}\times (z^2 + 9\times z) = \frac{z\times \left(9 + z\right)}{\left(z + 9\right)\times \left(z + 7\times (-1)\right)}
|
-518 |
e^{10*\dfrac{3*i*\pi}{2}} = (e^{\frac{3*i*\pi}{2}})^{10}
|
-29,339 |
\left(2 y + 5\right) (2 y + 5 (-1)) = \left(2 y\right)^2 - 5 5 = 4 y^2 + 25 (-1)
|
-15,264 |
\frac{k}{\frac{1}{k^8} s^8}s^2 = \dfrac{ks^2}{\frac{1}{\frac{1}{s^8} k^8}}1
|
22,969 |
f^k \cdot f^m = f^{k + m}
|
-6,003 |
\frac{1}{35 + B\cdot 5}\cdot 3 = \frac{1}{5\cdot (B + 7)}\cdot 3
|
27,707 |
\dfrac{1}{exp(A)} = exp(-A)
|
21,114 |
151657\cdot 27099 = (1519\cdot 41 + 1541\cdot 58)\cdot \left(-1519\cdot 41 + 1541\cdot 58\right)
|
13,089 |
1/9 + 5/216 + 2/27 + 4/27 = 77/216
|
45,104 |
51 = 153/3
|
-30,443 |
8 = 3 \cdot 2 \cdot 2 + A = 12 + A
|
24,924 |
\cos{2\theta} = -2\sin^2{\theta} + 1
|
-18,981 |
37/40 = \frac{A_x}{64 \pi}*64 \pi = A_x
|
-4,480 |
(x + 2)\cdot \left(4 + x\right) = 8 + x^2 + x\cdot 6
|
-26,470 |
16 \cdot x = 2 \cdot 8 \cdot x
|
30,821 |
-2016^{155}/2 + 2016^{155} = \frac{1}{2}\cdot 2016^{155}
|
30,727 |
c = c\cdot (r_1\cdot a + p_1\cdot b) = c\cdot r_1\cdot a + c\cdot p_1\cdot b
|
7,341 |
z + 1 = w \Rightarrow z = (-1) + w
|
7,054 |
-\cos(X) = \sin\left(\frac{\pi}{2} \cdot 3 - X\right)
|
27,061 |
5/12*4*2 = \dfrac{10}{3}
|
-19,105 |
1/5 = X_p/(36\cdot \pi)\cdot 36\cdot \pi = X_p
|
28,196 |
\sin(u)\cdot \cos(u)\cdot 2 = \sin(2\cdot u)
|
-9,565 |
0.6 = \dfrac{1}{10}*6 = 3/5
|
23,629 |
x + u = (u/2 + \frac{x}{2})\cdot 2
|
21,164 |
3 + f \cdot 2 - 3 \cdot f + f \cdot 4 = 0 \implies -1 = f
|
13,136 |
-n \cdot n + (n + 1)^2 = 2\cdot n + 1
|
28,712 |
\frac{1}{16} + \frac18 = \frac16 + \frac{1}{48}
|
21,209 |
2\sin(\tau) \cos\left(\tau\right) = \sin(2\tau)
|
7,552 |
\dfrac{x}{a} \Rightarrow \frac{x}{a}
|
20,021 |
y = (m/\delta)^{y + (-1)} = \frac{\delta}{m}*(m/\delta)^y
|
20,658 |
\sqrt{1 - \cos\left(4*x\right)} = \sqrt{2*\sin^{22}(x)} = \sqrt{2}*|\sin(2*x)|
|
-4,057 |
4*z^3 = 4*z^3
|
21,941 |
\left(l + 1\right)^2 - \left(l + (-1)\right)^2 = l^2 + 2 \cdot l + 1 - l^2 + 2 \cdot l + (-1) = 4 \cdot l
|
-26,579 |
z^2 + 64*(-1) = -8^2 + z^2
|
25,648 |
\cos(e + f) = -\sin(f) \sin(e) + \cos(f) \cos(e)
|
52,835 |
920 = 40\cdot 23
|
14,641 |
\frac{1}{\tan^2(z) + 1}\cdot \tan^2(z) = \sin^2(z)
|
1,728 |
-\pi \geq -(f - a)\Longrightarrow f - a \geq \pi
|
13,039 |
(2 - m) (2 - m) = (-(m + 2 (-1)))^2 = \left(-1\right)^2 (m + 2 (-1))^2 = \left(m + 2 (-1)\right)^2
|
25,939 |
0 = -162 + 486 + 648\cdot \left(-1\right) + 324
|
9,374 |
6^2 + 8^2 + 24^2 = 4\cdot 13 \cdot 13
|
18,426 |
14 = 2\cdot 7 = \left(1 + \sqrt{-13}\right)\cdot \left(1 - \sqrt{-13}\right)
|
21,066 |
n + (-1) + l = n + l + (-1)
|
16,703 |
\dfrac{4!}{2!*2!}*10*5! = 7200
|
-11,955 |
13/15 = \dfrac{s}{12 \cdot π} \cdot 12 \cdot π = s
|
5,032 |
h^{k_2 + k_1} = h^{k_1} \cdot h^{k_2}
|
-19,105 |
1/5 = \frac{Y_q}{36\cdot \pi}\cdot 36\cdot \pi = Y_q
|
8,530 |
\dfrac{1}{N^N} \cdot (N + (-1))^N = (\frac{1}{N} \cdot (N + \left(-1\right)))^N = (1 - 1/N)^N
|
4,802 |
\frac{4}{100} \cdot z = 0.04 \cdot z
|
25,909 |
\frac1n*n_2*x*n_1 = \frac1n*n_2*n_1*x
|
22,324 |
\dfrac{h}{h + (-1)} = \frac{1}{h + (-1)}*(h + \left(-1\right)) + \frac{1}{h + (-1)} = 1 + \frac{1}{h + (-1)}
|
-17,139 |
8 = 8\cdot 3\cdot l + 8\cdot (-4) = 24\cdot l - 32 = 24\cdot l + 32\cdot (-1)
|
17,462 |
(c + e)*x = x*e + c*x
|
9,555 |
2 \cdot a - (6 \cdot b + 2 \cdot (-1)) \cdot a = 4 \cdot a - 6 \cdot a \cdot b = \left(4 - 6 \cdot b\right) \cdot a
|
4,617 |
6 \cdot y - 2 \cdot x = (-x + 3 \cdot y) \cdot 2
|
16,471 |
\dfrac{1}{4^4} \cdot 4! = \tfrac{3}{32}
|
5,041 |
3/2009 = \frac{1}{2009} + 2/2008 \cdot \frac{2008}{2009}
|
43,203 |
1 + \sin^2{\theta} = \tfrac{1}{2}\cdot (3 - 1 - 2\cdot \sin^2{\theta}) = (3\cdot \theta - \sin{\theta}\cdot \cos{\theta})/2
|
33,829 |
\frac1y = \frac{\sin{y}}{\sin{y}} \cdot \frac1y
|
-6,135 |
\frac{3}{q \cdot q + q \cdot 3 + 70 \cdot (-1)} = \frac{1}{(q + 10) \cdot (q + 7 \cdot (-1))} \cdot 3
|
54,982 |
60 = 5 + 55
|
-24,447 |
\dfrac{170}{8 + 9} = 170/17 = \dfrac{170}{17} = 10
|
21,604 |
(T^{\frac{1}{2}})^2 = T
|
-16,349 |
7 \times 125^{\dfrac{1}{2}} = (25 \times 5)^{\frac{1}{2}} \times 7
|
-9,482 |
3*(-1) + a*12 = 3*(-1) + a*2*2*3
|
-2,411 |
6^{1 / 2}\cdot 9^{\frac{1}{2}} + 6^{\frac{1}{2}} = 3\cdot 6^{1 / 2} + 6^{1 / 2}
|
-176 |
\frac{7!}{6!*(7 + 6*(-1))!} = \binom{7}{6}
|
29,664 |
n\cdot 2 + \left(-1\right) = (1 + n)\cdot 2 + 3(-1)
|
-19,270 |
\frac{3}{5} \cdot \frac{9}{1} = 3 \cdot \frac{1}{5}/\left(\frac{1}{9}\right)
|
-11,990 |
2/15 = \frac{s}{12 \cdot π} \cdot 12 \cdot π = s
|
5,224 |
\tfrac{1/365\times 1/365}{365}\times 365 = \frac{1}{365^2}
|
-20,408 |
\frac{1}{35 + 5\times p}\times (p\times 4 + 28) = 4/5\times \frac{1}{7 + p}\times (p + 7)
|
23,016 |
-(g - \sqrt{5} \cdot b) = \sqrt{5} \cdot b - g
|
19,793 |
-y \cdot y + x^2 = (-y + x) \cdot (x + y)
|
-19,817 |
0.01\cdot (-122) = -\frac{122}{100} = -1.22
|
-5,412 |
2.56 \times 10 = \frac{1}{10^6} \times 25.6 = \frac{2.56}{10^5}
|
-4,569 |
\dfrac{x + 41 \cdot (-1)}{x^2 - x + 20 \cdot (-1)} = \frac{5}{x + 4} - \frac{4}{5 \cdot (-1) + x}
|
-7,984 |
\frac{1}{2\times i - 1}\times (i - 13) = \frac{-2\times i - 1}{-i\times 2 - 1}\times \frac{i - 13}{2\times i - 1}
|
-4,093 |
s^3*\frac{6}{5} = s^3*6/5
|
5,310 |
(\left(-1\right) + x^p) * (\left(-1\right) + x^p) = 1 + x^{p*2} - 2*x^p
|
29,170 |
1 + 2^{(-1) + k} + \left(-1\right) + 2^{k + (-1)} + (-1) = (-1) + 2^k
|
41,531 |
|C| = |C| \times |C| = |C \times C|
|
13,087 |
\operatorname{E}[W]^{2\cdot x + 1} = \operatorname{E}[W^{x\cdot 2 + 1}]
|
21,617 |
-8 + x\cdot 4 + d\cdot 2 = \dfrac{1}{d}\cdot (-8\cdot d + 4\cdot x\cdot d + d^2\cdot 2)
|
6,332 |
l = l + (-1) + 1 = l + 2(-1) + 2 = ... = \frac{1}{2}(l + 1) + \dfrac12(l + (-1))
|
323 |
(i*16)^{-1} = (4i)^{-1} - \frac{1}{16 i}3
|
46,960 |
2\cdot 11 = 22 = 10
|
-20,813 |
\frac{1}{-35}\cdot (-63\cdot z + 21\cdot (-1)) = (3\cdot (-1) - 9\cdot z)/(-5)\cdot 7/7
|
44,532 |
2^2 = 3 + 1
|
32,238 |
3^3-2^4=11
|
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